Calculate Cut Angle
Calculator for the angles that arise when an angle is cut. The angular sum in a triangle is 180 degrees and the angle of a straight line is also 180 degrees. From this, the new angles created when cutting off can be calculated. At a vertically cut angle, the section is perpendicular to the bisecting line, while in the case of the obliquely cut angle, it is not.
Vertically Cut Angle
At the vertically cut angle, the formulas are:
β = ( 180° - α ) / 2
γ = 180° - β
Obliquely Cut Angle
If the cut is in an angle δ, the four new angles are calculated from β and γ of the vertically cut angle:
β1 = β - (90° - δ)
β2 = β + (90° - δ)
γ1 = γ + (90° - δ)
γ2 = γ - (90° - δ)
This calculator first deals with a special case of the triangle, the isosceles triangle. This has two sides of equal length and therefore also two angles of equal measure. This simplifies the calculation. A general triangle, on the other hand, can have any type of side and angle, as long as the sum of the angles is 180 degrees and the lengths are allowed for given angles.
Three straight lines lying in a plane, none of which are parallel or coincident, and which do not intersect at a single point, always form a triangle. This is because the lines are infinitely long, and in Euclidean geometry, which is plane geometry, if two lines are neither parallel nor identical, they always intersect at a point. This follows from Euclid's famous parallel postulate. Such a triangle has a total of three angles, of which none or one, not more, is 90 degrees or greater.